let

i = the time the inlet pipe fills the pond alone, l>0

h = the time the hose fills the pond alone, h>0

the inlet pipe alone can complete the job in 1 hour less time than the hose alone

i = h - 1

inlet pipe and a hose together can fill the pond in 3 hours

the rate of the inlet +the rate of the hose = the together rate

1/i + 1/h = 1/3

plug i = h - 1 into the above equation

1/(h - 1) + 1/h = 1/3

by solving we find 2 roots

h1 = 6.54 hr

h2 = 0.46 hr

click here to see the step by step solution of the equation

Click to see all the steps

for h = 6.54 hr

i = h - 1 = 6.54 - 1 = 5.54 hr

for h = 0.46 hr

i = h - 1 = 0.46 - 1 = - 0.54 < 0 this is not the solution since we need i>0

the hose can fill the pond alone in 6.54 hours

the inlet pipe can fill the pond alone in 5.54 hours.